Integrating Visual and Mathematical Models for the Management of Interdependent Critical Infrastructures* Madhavi Chakrabarty Information Systems Department New Jersey Institute of Technology Newark, NJ, U.S.A.
David Mendonça Information Systems Department New Jersey Institute of Technology Newark, NJ, U.S.A.
[email protected]
Abstract – Critical infrastructures provide services essential to a nation’s economy and security. These systems are now viewed as interconnected and interdependent systems that must be managed over space and time. The central problem of the present line of research is how to develop computer-based tools to support the delivery of services provided by these infrastructures. This paper draws upon visualization and modeling sciences to develop a methodology for defining a set of visualization and visual tools for monitoring and managing interdependent critical infrastructure systems. An example is used to illustrate the steps in the methodology. Keywords: Interdependent critical infrastructure systems, systems modeling, visualization.
1
Introduction
Critical infrastructures are crucial for the economic well-being and security of a nation. The United States government has identified eight infrastructure systems as critical: emergency services; transportation; information and communications; electric power; banking and finance; gas and oil production, storage and transportation; water supply; and government. These services may not be degraded, whether by willful acts such as terrorism or by natural or random events such as earthquakes, design flaws or human errors [1]. Yet these infrastructures are now viewed as interconnected and interdependent systems of systems that must be managed through geographic space and over time. The focus of the work presented in this paper is on applying a structured modeling technique to the problem of designing an interface which infrastructure managers use to manage and monitor a set of interdependent infrastructures, This paper draws upon visualization and modeling sciences to present methodologies for building a set of visualizations and visual tools (or widgets) for monitoring and managing interdependent critical infrastructure systems. The methodology’s use is illustrated by applying it to an existing linear programming formulation of interdependent critical infrastructures.
*
0-7803-8566-7/04/$20.00 2004 IEEE.
[email protected]
2
Background
Critical infrastructure systems may be components of highly-coupled interdependent systems [2], with physical or logical connections amongst each other [3]. Because some activities, such as identifying and managing interdependencies, must be accomplished by two or more organizations, decision-making among various public and private organizations must be coordinated. Modeling is a fundamental human activity. In a seminal paper on the process of building models, Morris [4] proposed a number of hypotheses concerning how good models can be derived. Since then, there have been numerous developments in the art and science of modeling. An important area of growth is in the development of modeling languages. Over the years, modeling languages have matured with large-scale network optimization. A second area of growth is in the development of cognitive models of space and of models of spatial processes [5]. With the developments in these two areas, opportunities are arising for using modeling methodologies to develop cognitively-grounded models of spatial phenomena. Previous work in developing models of infrastructure includes proposed mathematical or linear programming representations of these systems [3, 6, 7]. These representations help in providing support and other improvements in system management. Simulation-based approaches to modeling have been implemented in private industry as well as national labs [2]. Other techniques of modeling that have been successfully implemented include network and graph models, geographic information systems and CASE tools [8, 9]. Such models add a layer between infrastructure managers or decision makers and the systems they monitor and control as shown in Figure 1. This leads to the question of how interdependent critical infrastructure systems may be represented in a form that supports managerial decisionmaking about them.
3
Decision Makers
Visual Model
Mathematical Model
Physical World
Figure 1: Model-mediated Interaction A challenge taken up in this paper is to develop visually-based tools for analyzing, manipulating and controlling these models. Examples of such uses are found in various domains [10-13]. An exploration of the role of visualization in infrastructure management is appropriate for many reasons. Prior research has shown that visual models capitalize on a fundamental, native expertise of humans: the ability to solve complex problems by reasoning with graphical representations. Visual models can offer advantages over purely lexical models by increasing interpretability and reducing cognitive load, thus enabling decision makers to devote additional cognitive resources to problem solving [14]. In addition to their usefulness as representations, visualizations are also useful in control. Visualization widgets, defined as visual tools for controlling or processing a visual model, enables users to interact with models [15] . Examples of widgets include menus, control buttons, sliders for controlling through a computer interface [16]. The current emphasis of visualization is on representation and not on control. The integration of models of critical infrastructure systems with GIS (Geographic Information Systems) leads to a wide range of benefits to investigate the behavior of spatio-temporal processes through simulation studies that incorporate human decision makers. Currently most models are based on environmental models (e.g., transportation, hydraulic etc.), which follow directly from the human perception of infrastructures being a part of the environment. With the increasing capabilities of computer systems (including Internet), has come the opportunity to ease the process of developing and rendering visualizations [17]. This has also lead to the model becoming more interactive, real time and has been successful in leveraging the added benefits of concurrent usage of the model for decision-making. Additionally, prior research on visualization for model analysis, manipulation and control has shown its applicability for single systems, suggesting that it might also be applied to systems of systems. Finally, in practice—as in the response to the 2001 World Trade Center attack—system visualizations such as maps are used extensively in managing critical infrastructures [18].
Research
This research is concerned with developing visualization of the mathematical models that support interdependent infrastructure systems. A suitable visualization will enable decision makers to act on the visualization as if they were acting on the system itself. A hypothesis of the current research is that use of visualization will enable decision makers to effectively harness the power of mathematical models by (i) increasing model comprehensibility and (ii) enabling effective sharing and analysis of the underlying physical systems. This paper summarizes and briefly illustrates a methodology for developing visual models for use in monitoring and controlling interdependent critical infrastructure systems, both of which are crucial for normal and extenuating operating conditions. The present domain of the problem is to represent the mathematical models already available for the infrastructure systems in visual models to aid decision making of managers. The mathematical representation of the critical infrastructures defines them in terms of their position, capacities, properties and special characteristics. Therefore the visualization should incorporate all the parameters of the mathematical models, as well as the mode (i.e., system state) Two sets of results are presented in the following section. First, a methodology for constructing a set of visualization and visual tools is derived based on prior research in modeling science. Second, the methodology’s application is illustrated for a hypothetical interdependent critical information system. The visualization of the mathematical models of this hypothetical system includes (i) a representation of the infrastructures under normal conditions, (ii) the changed infrastructure visualization in the event of a disruption and (iii) restoration strategies for bringing the system as close to the normal model as possible.
4
Results
The intention of this methodology is to produce a vocabulary and grammar for representing and manipulating mathematical models of interdependent critical infrastructures [19].
4.1
Method
Various modeling approaches [11, 20-23] influence the design of the methodology. In particular, Morris’ [4] seminal work on the process of modeling is applied to create a visual model that can be used for monitoring and controlling infrastructures as represented in a mathematical model. Because the process of modeling is an iterative one [4], the methodology includes formulating the steps to create a model. The model can further be refined in subsequent steps based on feedback to the model developed. Steps in the methodology include-
(i)
Factoring the problem into sub-problems.
(ii)
Establishing a clear statement of deductive objectives for each sub-problem.
4.1.4
(iii) Developing analogies. (iv)
4.1.1
Verifying with example.
Factoring problems
the
an
illustrative/
problem into
numeric
sub-
Activities in critical infrastructure management following a disruption include prioritizing service restoration, identifying alternate physical components or activities, and restoring service levels to pre-disruption levels. Managers must also decide on the minimum or optimal resources, identify interdependencies, contain disruption and delineate the boundaries of the impact.
4.1.2
Establishing a clear statement of deductive objectives for each subproblem
To prioritize service restoration and schedule efforts, geographic information of the access points to the system and the locations of alternate resources (ex, alternate power supply) need to be known or discovered. The model should identify appropriate available resources, capabilities, distance and ease of procurement of the resources. As an example, for an alternate power supply source, it is necessary to know its output, coverage area, portability and dependencies (e.g., for fuel). Information of the infrastructure, services it provides under normal operations and its interdependencies on other infrastructures should either be known or deducible for containing the extent of damages to isolate the disrupted service and prevent the extent of the disruption.
4.1.3
Developing analogies
The problems are considered analogous to a network or graph to enable the managers to optimize restoration efforts, allocate resources and improvise decisions over time. It also helps in scheduling effort to allocate resources to a location at an optimized cost (or time). A topological or geographical area map shows the impact or extent of a disruption as well as the boundaries containing it. Appropriate visualizations may be readily available for some aspects of these analogous relationships.
Verifying with an illustrative/numeric example
To reduce complexity, systems can be divided into component systems or sub-systems. Each sub-system is modeled as a network system [3] consisting of nodes, and arcs connecting the nodes. The critical infrastructure systems can either be depicted as a point infrastructure (a telephone pole or power generation plant) or as a line structure (roadways or water supply lines). The nodes can be a demand, supply or transshipment nodes and should be capable of denoting the location, temporal behavior, physical characteristics, status, and the organization responsible for maintaining the system. Arcs connecting the nodes should likewise be able to denote the direction of transfer, rate of transfer, duration, capacity and content. The normal operations model depicts the location of the system relative to other infrastructure on a geographic scale including the services of the system, its dependencies to other infrastructures, and activities such as generation, transfer and termination of the service. Limitations and capabilities of each infrastructure are shown as properties of that node. Various properties like shape, color, boundary and highlights have been used to represent different features [24]. These features define a structure, its properties and behavior. Physical characteristics of a node are represented as a list. The status of the node is the darkness of the color on the grayscale (white - 100% and black - 0% operational). An icon is used to represent the responsible organization. Time can be represented as a point on a slider denoting the timeline or as a dial in the corner of the screen. Interdependence between structures is represented as arcs with the line ends denoting the type of interdependency. Arrows are used to show input; bars at the end of arcs represent exclusive-or; dots/ bullets denote shared and no mark indicates interdependent. No interdependence is shown by the absence of the line. Relative position of the systems is maintained by positioning them on their geographical co-ordinates. For maintaining clarity, shared or co-located infrastructures are placed next to one another.
4.2
Illustrative example
Selected steps in the methodology are applied to an example (adapted from [3]) involving interdependent telecommunications and power infrastructures. Assume that a telecommunications company is responsible for a switching station, which is used to route calls through a network. Power from an electric utility’s transformer is required to operate the switching station, creating an input interdependency [3] from power to telecommunications. The raw data that must be visualized include data about the transformer (Table 1) consisting of identifying information (“ID”), geographic location (“loc”), state (e.g., 1 means the transformer is functioning), current operating level and rated capacity. This tuple is assumed to describe the transformer’s state at some time t. Similar tuples
would be available for other system components and activities over time, all of which would be stored in databases for access by decision makers. Table 1. Tuple for Transformer A ID Tr. A
Loc. 40.75N,74W
State 1
Curr.Oper.Level 5000 kw
Rated Cap. 6500 kw
An analogy (step 4.1.3) is made between this subsystem and a network having flows [3]: components (such as the switching station) are represented as nodes, which represent components of demand, supply or transshipment. Links between nodes represent channels through which infrastructure products (such as power) move. An initial visualization is shown in Figure 2.
Consider the case of an electric transformer failure resulting in power loss at the telephone switching station and subsequently to the telephone service. Figure 4 depicts the model after the failure of one transformer. The effected nodes change to a non-functioning representation (100% dark scale). The nodes that are still functional are shown functioning at normal levels. The service level of the effected nodes also drops below. The geographic representation helps in finding the location of the two systems from the model. Since the shade of each node denotes the operating levels, the levels after disruption would have fallen to levels much lower than normal levels (-ve). This change would indicate the impacted nodes and hence the extent of service disruption.
Transformer Demand
Switch
Figure 2: Initial Model Visualization To refine this visualization, the mathematical model of the system is first broken down into a set of constituent components (step 4.1.1). Elements of the visualization convey the location, physical characteristics, status and the organization responsible for the components (step 4.1.2). This information is displayed over time, since over time the status of the network may change. 0 5600 56
78
0
0
0 78
56
0 0 0 0
28
Figure 3: Model Visualization (normal) at Time t In the refined visualization (Figure 3), an initial visual vocabulary and grammar are presented to describe the state of the system at some time t. A square denotes a transmission service, a circle denotes utilization and a hexagon denotes monitoring units. Icons indicate the organization responsible for a component (e.g, a lightning symbol in a square represents a power transformer and a lightning symbol in a hexagon represents a SCADA facility). The bar below each service denotes the current operating level compared to the capacity of the system. The capacity of the unit appears on the right of the bar. Arrows denote input interdependency between services. The number on the arrow denotes the demand/shortage, with negative numbers indicating unmet demand. A normal functioning system is depicted in Figure 3.
Figure 4: Model Visualization After Disruption The next step would be to locate the source of failure. The property of the arcs helps navigate the source of the problem or the starting point of the disruption. If T is the demand node, and it has failed, we can traverse up the dependency path and see the transshipment node; the capacity of this node would also have come down. Therefore, traverse up to the power generator node. If the current status of this node is also below normal, then the power generator is the source of the problem otherwise the first transshipment node operating below normal is the source of the problem. Since the dependency arcs help to trace the source of failure, each dependency has to be presented in a different way. Another piece of information required by the manager is the cause of the problem in the system. An electric transformer can fail due to various conditions (e.g., heating of coil, disruption of a structure, snapping of a wire). This information is usually available in the SCADA system. This parameter can also be a part of the physical characteristic of the system. If the SCADA system was up at the time of disruption, the disruption would appear as an alarm on the SCADA node. The alarm can be a sound or flashing the node thereby seeking attention of the decision makers. Further iterations of the methodology refine the visualizations. For example, the analogy to network flows (step 4.1.3) suggests that arcs connecting the nodes should be able to denote the direction of transfer, rate of transfer, duration, capacity and content. These are represented as properties on the arc. Additional refinements can include developing ways to evaluate and
represent other properties of the interdependency and underlying assumptions and providing a set of symbols and grammars to build a concise and interactive model.
5
Discussions and Conclusions
This paper presents a methodology to visualize critical interdependent infrastructure systems, to enable better understanding of the complexities in the interdependence as well as aid them in decision-making, manipulating and controlling to help them in addressing emergency concerns that may arise. The visualization model of the interdependent critical infrastructure is expected to display alternate feasible solutions based on unmet demands, provide a restoration strategy, a routing plan and an optimization of restoration strategies. This can be achieved by using different path or views. An extension to the model will enable managers to interact with the system to support/reject selections. The visualization can be enhanced to produce activity logs, maps, after action reports for later evaluation and refining the model. To incorporate manipulation, control and interaction, different views of the system can be represented. These views include a normal functioning view, including input output view, data flow view and abnormal or disrupted view (e.g., impact view, unmet demand view, restoration planning view and feasible solution view). Provision to switch between an overview and detailed views are provided using zoom and filter features. In the event of any disruption to a component of an interdependent infrastructure, the visualization should allow the manager to interact to depict disruption, specify priorities and additional resources. This in turn will modify the visualization of the infrastructures to depict the changes in capabilities, supply, transshipment or demand of resources and the modified interdependence. Temporal changes resulting from a disruption of an interdependent infrastructure can be modeled using the manager’s inputs or built in rules in the system. For example, if we know that the water supply of a structure has is broken, but the infrastructure has a reserve for two hours of demand, then a rule inbuilt in the system can depict this shortfall after the time period. Currently the representation is a two dimensional and may fail to capture the three dimensional nature of most critical infrastructure systems. Even emergency workers are traditionally used to viewing systems in different ways. Evaluating the system can help understand the implication of the suggested visualization on the users of the system. There are many external factors that also influence decision-making of the managers. Such factors are considered out of scope of this paper. Therefore, when presenting visualization, the boundaries of the visualization have to be defined. The inherent complexity and spatio-temporal qualities of interdependent critical infrastructure systems make them ideal candidates for complexity reduction through visualization. This paper presents and illustrates a methodology for developing
visualizations for monitoring and control of such systems. The approach capitalizes on advances in modeling science while harnessing the core human capability of visual problem solving. The results of the implementation of this methodology should be of broad interest to researchers concerned with communicating the substance and behavior of mathematical models to decision makers, as well as to practitioners who must monitor and control these systems. Future work will focus towards implementation and evaluation of the methodology and the model created. Evaluation process includes evaluating the soundness of theory as well as the usability of the model by the intended users. Evaluating the ease of use of the system will focus on how effective visualization will be for users and whether the visualization developed helps the decision makers in the way as proposed by the paper. Evaluation of the model is intended to contribute to the model completeness and robustness and lead to improvements in decision made with the models. Evaluating the model outputs (such as recommendations) can be done with the help of domain experts. The evaluation phase may result in the development of a feedback loop to subsequently address any detail or unanticipated provisions that may have been missed out in this framework.
6
Acknowledgement
This research has been supported by National Science Foundation Grant CMS-0301661.
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